Sending out a company-wide email about your leaving that very company to thank people you don't even know for helping you out, while at the same time asking if anyone else can help you find a job.

Pulling a Kobie style email:
I have a few positions lined up for when my contract is over but nothing that is set in stone as of yet, if you know anyone/where that is looking for__, please by all means, send the info my way, I'd like as many options available as I can get.